A New Collocation Scheme Using Non-polynomial Basis Functions
In this paper, we construct a set of non-polynomial basis functions from a generalised Birkhoff interpolation problem involving the operator: Lλ=d2/dx2−λ2Lλ=d2/dx2−λ2 with constant λ.λ. With a direct inverting the operator, the basis can be pre-computed in a fast and stable manner. This leads to...
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| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/85589 http://hdl.handle.net/10220/43728 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | In this paper, we construct a set of non-polynomial basis functions from a generalised Birkhoff interpolation problem involving the operator: Lλ=d2/dx2−λ2Lλ=d2/dx2−λ2 with constant λ.λ. With a direct inverting the operator, the basis can be pre-computed in a fast and stable manner. This leads to new collocation schemes for general second-order boundary value problems with (i) the matrix corresponding to the operator LλLλ being identity; (ii) well-conditioned linear systems and (iii) exact imposition of various boundary conditions. This also provides efficient solvers for time-dependent nonlinear problems. Moreover, we can show that the new basis has the approximability to general functions in Sobolev spaces as good as orthogonal polynomials. |
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